This invention relates to feedback control.
In an example of a feedback control system, FIG. 1 shows a block diagram of a power converter 10 which accepts power from an input voltage source 14, of value Vin, and delivers power to a load 18 at a regulated load voltage Vout. Output voltage regulation is accomplished by negative feedback. An error voltage, Ve 34, representing the difference between a reference voltage 32 (indicative of the desired setpoint value for the output voltage Vout) and a measurement of Vout (the voltage, Vd 31, delivered by the divider 24), is fed to a controller 28 which delivers a control signal, Vcont 22, to the power conversion stage 12. If Vd is above Vref, Vcont decreases; if Vd is below Vref, Vcont increases. The value of Vcont is indicative of the value of the parameter which controls the output of the power conversion stage 12. For example, in a pulse-width-modulated (PWM) power conversion scheme, Vcont is indicative of duty cycle; in a zero-current switching scheme, Vcont is indicative of operating frequency. An increase in Vcont increases the power throughput of the power conversion stage, and vice versa.
Issues relating to closed-loop stability and both the steady-state and transient response characteristics of closed-loop feedback control systems are well documented. In this regard, the open-loop characteristics (e.g., the open-loop gain and phase shift as a function of frequency) of the feedback control system 10 are important. Conventionally, the design of closed-loop systems involves understanding the gain/phase characteristics of the different elements within the loop and designing a "linear" controller (in which gain is not a function of operating point; e.g., in FIG. 1, the incremental change in Vcont which results from a fixed incremental change in Ve will be the same irrespective of the average values of Ve and Vcont) which, when combined with other loop elements, results in an open-loop gain/phase characteristic which satisfies some set of predefined steady-state and transient performance criteria. Thus, for example, the controller might simply consist of a linear amplifier whose gain/phase characteristics are adjusted to provide an overall open-loop gain vs. frequency characteristic 36 of the kind shown in FIG. 2. The open-loop gain is designed to be relatively constant and equal to A1 up to a frequency f1. Above that frequency the gain is rolled off so that the gain and phase (the phase is not shown in the Figure) margins at crossover (e.g., the frequency at which the gain Aol=1) are consistent with stable closed-loop operation.
Alternatively, controller 28 might be modified, as shown in FIG. 3, to provide an overall open-loop gain characteristic 38 like the one shown in FIG. 4. In controller 28, amplifier 42 has a very high DC gain which rolls off with frequency (e.g., an integrator). In the closed-loop system, this amplifier will adjust its output, Veq, to an average value which forces the average value of the system error, Ve, to zero, thereby ensuring very accurate regulation of the converter DC output voltage, Vout. Veq is summed with the output of another linear amplifier 40 which is designed so that, when it is combined with other loop elements, the result is an open-loop gain characteristic as shown in FIG. 4. The high gain of the integrating amplifier dominates below a frequency fo. Above fo the linear amplifier dominates, providing both a region of relatively high "midband" gain (e.g., between frequencies f0 and f1) and a controlled rolloff in gain above f1 to ensure that the gain (and phase) margin at crossover (e.g., the frequency, f2, at which the gain Aol=1) are consistent with stable closed-loop operation.
In many applications the open-loop gain characteristic will change with both system operating point and environmental factors. For example, a broad class of PWM power conversion stages exhibit a gain characteristic which is proportional to converter input voltage, Vin. This means that if a system using such a converter is designed to operate over a 4:1 range in input voltage, the open-loop gain will vary at least by this amount as Vin varies over its range. Gain variations with operating conditions (e.g., Vin, power output), as well as nonlinear gain characteristics, are exhibited by other types of power conversion stages, such as zero-current switching converters. In nonideal systems the normal tolerance variations in system components, losses in energy storage elements, and dependencies of component characteristics on environmental factors, such as temperature, will also affect open-loop gain.
As a result, in many applications the open-loop gain cannot be characterized by a single plot of the kinds shown in FIGS. 2 and 4. Instead, the open-loop gain will exhibit variations (e.g., as illustrated by the family of gain plots, 38a-38d, in FIG. 5) that result from changes in system operating point and environment. As the open-loop gain varies, the attendant variations in low frequency and midband gain, crossover frequency, and gain/phase margins, will alter both the closed-loop performance and stability characteristics of the closed-loop system. Thus, conventional feedback control system design involves trading off closed-loop performance under a variety of operating conditions to ensure stable closed-loop operation under "worst-case" conditions.
Summary of the Invention
In general, in one aspect, the invention features a closed-loop feedback system having first and second gain elements. The first gain element has a transfer function such that Xd=Kg*(Xcont).sup.z, where Xcont is a control variable input signal of the first gain element, Xd is a controlled variable output signal of the first gain element, and Kg and z are independent of Xcont. The second gain element has a transfer function h1 such that Xcont=h1(Xe) where Xe is a control variable input signal of the second gain element and Xcont is a controlled variable output signal of the second gain element. The function h1 is of a form which satisfies [1/h1(Xe)]*[.delta.h1(Xe)/.delta.Xe]=Ke, where Ke is independent of Xe.
Implementations of the invention include the following features. The function h1 may be of the form h1(Xe)=Kx*exp(Ke*Xe) where Kx and Ke are independent of Xe. An input to the system may be a setpoint value, Xref, indicative of a desired value for an output signal, Xd, of the system. The system may have an open-loop gain, Aol, essentially equal to z*Ke*Xd. The gain of the second gain element may be proportional to its average output signal. The second gain element may include circuitry comprising a gain variable amplifier having a gain control input, and a control circuit having a gain control output connected to the gain control input of the gain variable amplifier. The control circuit may include a high-gain amplifier. The high-gain amplifier may have a bandwidth narrower than the bandwidth of the open-loop characteristic of the system. Outputs of the gain variable amplifier and the control circuit may be summed in a summing element. Inputs of the gain variable amplifier and the control circuit may be connected to receive the same input signal. A system input signal may be an error signal, Xe, indicative of the degree to which an output of the system, Xd, differs from a predetermined setpoint value, Xref, which is an input to the system. The control circuit may include an integrator, or a low pass filter. The low-pass filter may have an output connected to the gain control input of the gain variable amplifier, and the low-pass filter may have an input connected to an output of the gain control amplifier.
The first gain element may include a power converter connected between a source and a load. The power converter may have a controlled variable frequency of operation and the frequency of operation may be controlled based on a control signal received at an input of the power converter. The second gain element may have an input connected to the output of the power converter, and an output connected to the control input of the converter. The controller may include an isolation element for galvanically isolating the output of the controller from the input of the controller. The isolation element may include a magnetic coupler. The controller may include a gain adaptive amplifier, the gain of the gain adaptive amplifier being proportional to the average value of the output of the controller. The power converter may be a pulse-width modulated power converter. The power converter may be a zero-current switching power converter.
The open loop gain of the system may include a constant gain in a mid-band of frequencies, and, in other frequency bands, a gain that declines with increasing frequency. The first (second) gain element may include subelements and the transfer function of the first (second) gain element may be a composite transfer function. Xd, Xe, Xref, and Xcont may each be a voltage or a current.
In general, in another aspect, the invention features a power conversion system for converting power from a source for delivery to a load, the system including a closed-loop feedback system having a power converter and a controller with features as recited above.
In general, in another aspect, the invention features a method of causing a closed-loop feedback system to have a generally constant value of open-loop gain, by means of features recited above.
Among the advantages of the invention are the following.
Since variations in open-loop gain affect closed-loop system performance and stability, use of a controller which provides an open-loop gain characteristic (Equation 6) which is either invariant, or which varies very predictably, with changes in system operating point or environment, offers significant advantages. For example, use of such a controller provides for uniform, or very predictable, closed-loop system performance over a wide range of electrical and environmental operating conditions.
Other advantages and features will become apparent from the following description and from the claims.